Scaling laws of marine predator search behaviour

Controlling and optimizing the transport (search) efficiency with local information on a class of scale-free trees

The scale-free trees are fundamental dynamics networks with extensive applications in material and engineering fields owing to their high reliability and low power consumption characteristics. Controlling and optimizing transport (search) efficiency on scale-free trees has attracted much attention. In this paper, we first introduce degree-dependent weighted tree by assigning each edge (x,y) a weight wxy=(dxdy)θ, with dx and dy being the degree of nodes x and y, and θ being a controllable parameter. Then, we design a parameterized biased random walk strategy with the transition probability depending on the local information (the degree of neighboring nodes) and a parameter θ. Finally, we evaluate analytically the global mean first-passage time, which is an important indicator for measuring the transport (search) efficiency on the underlying networks, and find the interval for parameter θ where transport (search) efficiency can be improved on a class of scale-free trees. We also analyze the (transfinite) walk dimension for our biased random walk on the scale-free trees and find one can obtain arbitrary transfinite walk dimension in an interval by properly tuning the biased parameter θ. The results obtained here would shed light on controlling and optimizing transport (search) efficiency on objects with scale-free tree structures.

Multiple environmental stressors affect predation pressure in a tropical freshwater system

Environmental change can alter predator-prey dynamics. However, studying predators in the context of co-occurring environmental stressors remains rare, especially under field conditions. Using in situ filming, we examined how multiple stressors, including temperature and turbidity, impact the distribution and behaviour of wild fish predators of Trinidadian guppies (Poecilia reticulata). The measured environmental variables accounted for 17.6% of variance in predator species composition. While predator species differed in their associations with environmental variables, the overall prevalence of predators was greatest in slow flowing, deeper, warmer and less turbid habitats. Moreover, these warmer and less turbid habitats were associated with earlier visits to the prey stimulus by predators, and more frequent predator visits and attacks. Our findings highlight the need to consider ecological complexity, such as co-occurring stressors, to better understand how environmental change affects predator-prey interactions.

Dispersal and interbreeding as survival strategies for species exposed to environment change

The success of individual species under a change to the environment is dependent on a number of factors, which include the changes to habitat, competition with other species and adaptability. Here we investigate the impact of differing dispersal characteristics of two competing species responding to the change using an idealized spatio-temporal model. The rate of dispersion is given by a combination of the growth term and the form of the diffusion term, which is set to give either normal diffusion or anomalous (super) diffusion. The later is brought about by employing fractional diffusion and we characterize the population as being more adventurous than the population undergoing normal diffusion. The more adventurous population is found, not surprisingly, to reach and occupy uninhabited ground before the population undergoing normal diffusion can get there. Interbreeding is found to be important in that it can aid the spread of the less adventurous population preventing its extinction. The response to an abrupt environment change, taken here to be a change in the distribution of the growth rate, is dependent on the initial conditions, the dispersion characteristics, and the level of interbreeding, leading to very different intermediate and final states. Our results highlight instances when a particular dispersal strategy gives a population an edge over another. In the cases considered here we find states where the more adventurous population can dominate across the domain, the two populations exist in separate parts of the domain separated by fronts, and both populations coexist across the domain in the medium term with one or other of the populations dominating across the domain in the long term. Given the long time to reach equilibrium where one or other of the populations dominate, consideration needs to be put to the time scale of change, as sufficiently frequent change can allow coexistence. We demonstrate the need to include dispersion characteristics when considering the factors affecting the response of species to a change in the environment.

Smart active particles learn and transcend bacterial foraging strategies

Throughout evolution, bacteria and other microorganisms have learned efficient foraging strategies that exploit characteristic properties of their unknown environment. While much research has been devoted to the exploration of statistical models describing the dynamics of foraging bacteria and other (micro-) organisms, little is known, regarding the question of how good the learned strategies actually are. This knowledge gap is largely caused by the absence of methods allowing to systematically develop alternative foraging strategies to compare with. In the present work, we use deep reinforcement learning to show that a smart run-and-tumble agent, which strives to find nutrients for its survival, learns motion patterns that are remarkably similar to the trajectories of chemotactic bacteria. Strikingly, despite this similarity, we also find interesting differences between the learned tumble rate distribution and the one that is commonly assumed for the run and tumble model. We find that these differences equip the agent with significant advantages regarding its foraging and survival capabilities. Our results uncover a generic route to use deep reinforcement learning for discovering search and collection strategies that exploit characteristic but initially unknown features of the environment. These results can be used, e.g., to program future microswimmers, nanorobots, and smart active particles for tasks like searching for cancer cells, micro-waste collection, or environmental remediation.

Spatial prey availability and pulsed reproductive tactics: Encounter risk in a canid-ungulate system

Predation risk is a function of spatiotemporal overlap between predator and prey, as well as behavioural responses during encounters. Dynamic factors (e.g. group size, prey availability and animal movement or state) affect risk, but rarely are integrated in risk assessments. Our work targets a system where predation risk is fundamentally linked to temporal patterns in prey abundance and behaviour. For neonatal ungulate prey, risk is defined within a short temporal window during which the pulse in parturition, increasing movement capacity with age and antipredation tactics have the potential to mediate risk. In our coyote-mule deer (Canis latrans-Odocoileus hemionus) system, leveraging GPS data collected from both predator and prey, we tested expectations of shared enemy and reproductive risk hypotheses. We asked two questions regarding risk: (A) How does primary and alternative prey habitat, predator and prey activity, and reproductive tactics (e.g. birth synchrony and maternal defence) influence the vulnerability of a neonate encountering a predator? (B) How do the same factors affect behaviour by predators relative to the time before and after an encounter? Despite increased selection for mule deer and intensified search behaviour by coyotes during the peak in mule deer parturition, mule deer were afforded protection from predation via predator swamping, experiencing reduced per-capita encounter risk when most neonates were born. Mule deer occupying rabbit habitat (Sylvilagus spp.; coyote's primary prey) experienced the greatest risk of encounter but the availability of rabbit habitat did not affect predator behaviour during encounters. Encounter risk increased in areas with greater availability of mule deer habitat: coyotes shifted their behaviour relative to deer habitat, and the pulse in mule deer parturition and movement of neonatal deer during encounters elicited increased speed and tortuosity by coyotes. In addition to the spatial distribution of prey, temporal patterns in prey availability and animal behavioural state were fundamental in defining risk. Our work reveals the nuanced consequences of pulsed availability on predation risk for alternative prey, whereby responses by predators to sudden resource availability, the lasting effects of diversionary prey and inherent antipredation tactics ultimately dictate risk.

Intermittent Search, Not Strict Lévy Flight, Evolves under Relaxed Foraging Distribution Constraints

AbstractThe survival of an animal depends on its success as a forager, and understanding the adaptations that result in successful foraging strategies is an enduring endeavour of behavioral ecology. Random walks are one of the primary mathematical descriptions of foraging behavior. Power law distributions are often used to model random walks, as they can characterize a wide range of behaviors, including Lévy walks. Empirical evidence indicates the prevalence and efficiency of Lévy walks as a foraging strategy, and theoretical work suggests an evolutionary origin. However, previous evolutionary models have assumed a priori that move lengths are drawn from a power law or other families of distributions. Here, we remove this restriction with a model that allows for the evolution of any distribution. Instead of Lévy walks, our model unfailingly results in the evolution of intermittent search, a random walk composed of two disjoint modes-frequent localized walks and infrequent extensive moves-that consistently outcompeted Lévy walks. We also demonstrate that foraging using intermittent search may resemble a Lévy walk because of interactions with the resources within an environment. These extrinsically generated Lévy-like walks belie an underlying behavior and may explain the prevalence of Lévy walks reported in the literature.

Lévy flights and Lévy walks under stochastic resetting

Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. We demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also in the presence of heavy-tailed, Lévy-type, α-stable noise. However, the width of the domain where resetting is beneficial depends on the value of the stability index α determining the power-law decay of the jump length distribution. For heavier (smaller α) distributions, the domain becomes narrower in comparison to lighter tails. Additionally, we explore connections between Lévy flights (LFs) and Lévy walks (LWs) in the presence of stochastic resetting. First of all, we show that for Lévy walks, the stochastic resetting can also be beneficial in the domain where the coefficient of variation is smaller than 1. Moreover, we demonstrate that in the domain where LWs are characterized by a finite mean jump duration (length), with the increasing width of the interval, the LWs start to share similarities with LFs under stochastic resetting.

Size-dependent self-avoidance enables superdiffusive migration in macroscopic unicellulars

Many cells face search problems, such as finding food, mates, or shelter, where their success depends on their search strategy. In contrast to other unicellular organisms, the slime mold Physarum polycephalum forms a giant network-shaped plasmodium while foraging for food. What is the advantage of the giant cell on the verge of multicellularity? We experimentally study and quantify the migration behavior of P. polycephalum plasmodia on the time scale of days in the absence and presence of food. We develop a model which successfully describes its migration in terms of ten data-derived parameters. Using the mechanistic insights provided by our data-driven model, we find that regardless of the absence or presence of food, P. polycephalum achieves superdiffusive migration by performing a self-avoiding run-and-tumble movement. In the presence of food, the run duration statistics change, only controlling the short-term migration dynamics. However, varying organism size, we find that the long-term superdiffusion arises from self-avoidance determined by cell size, highlighting the potential evolutionary advantage that this macroscopically large cell may have.

Exploring the interplay between small and large scales movements in a neotropical small mammal

We record and analyze the movement patterns of the marsupial Didelphis aurita at different temporal scales. Animals trajectories are collected at a daily scale by using spool-and-line techniques and, with the help of radio-tracking devices, animals traveled distances are estimated at intervals of weeks. Small-scale movements are well described by truncated Lévy flight, while large-scale movements produce a distribution of distances which is compatible with a Brownian motion. A model of the movement behavior of these animals, based on a truncated Lévy flight calibrated on the small scale data, converges towards a Brownian behavior after a short time interval of the order of 1 week. These results show that whether Lévy flight or Brownian motion behaviors apply, will depend on the scale of aggregation of the animals paths. In this specific case, as the effect of the rude truncation present in the daily data generates a fast convergence towards Brownian behaviors, Lévy flights become of scarce interest for describing the local dispersion properties of these animals, which result well approximated by a normal diffusion process and not a fast, anomalous one. Interestingly, we are able to describe two movement phases as the consequence of a statistical effect generated by aggregation, without the necessity of introducing ecological constraints or mechanisms operating at different spatio-temporal scales. This result is of general interest, as it can be a key element for describing movement phenomenology at distinct spatio-temporal scales across different taxa and in a variety of systems.

Bioenergetic modelling of a marine top predator's responses to changes in prey structure

Determining how animals allocate energy, and how external factors influence this allocation, is crucial to understand species' life history requirements and response to disturbance. This response is driven in part by individuals' energy balance, prey characteristics, foraging behaviour and energy required for essential functions. We developed a bioenergetic model to estimate minimum foraging success rate (FSR), that is, the lowest possible prey capture rate for individuals to obtain the minimum energy intake needed to meet daily metabolic requirements, for female sperm whale (Physeter macrocephalus). The model was based on whales' theoretical energetic requirements using foraging and prey characteristics from animal-borne tags and stomach contents, respectively. We used this model to simulate two prey structure change scenarios: (1) decrease in mean prey size, thus lower prey energy content and (2) decrease in prey size variability, reducing the variability in prey energy content. We estimate the whales need minimum of ~14% FSR to meet their energetic requirements, and energy intake is more sensitive to energy content changes than a decrease in energy variability. To estimate vulnerability to prey structure changes, we evaluated the compensation level required to meet bioenergetic demands. Considering a minimum 14% FSR, whales would need to increase energy intake by 21% (5-35%) and 49% (27-67%) to compensate for a 15% and 30% decrease in energy content, respectively. For a 30% and 50% decrease in energy variability, whales would need to increase energy intake by 13% (0-23%) and 24% (10-35%) to meet energetic demands, respectively. Our model demonstrates how foraging and prey characteristics can be used to estimate impact of changing prey structure in top predator energetics, which can help inform bottom-up effects on marine ecosystems. We showed the importance of considering different FSR in bioenergetics models, as it can have decisive implications on estimates of energy acquired and affect the conclusions about top predator's vulnerability to possible environmental fluctuations.

Learning how to find targets in the micro-world: the case of intermittent active Brownian particles

Finding the best strategy to minimize the time needed to find a given target is a crucial task both in nature and in reaching decisive technological advances. By considering learning agents able to switch their dynamics between standard and active Brownian motion, here we focus on developing effective target-search behavioral policies for microswimmers navigating a homogeneous environment and searching for targets of unknown position. We exploit projective simulation, a reinforcement learning algorithm, to acquire an efficient stochastic policy represented by the probability of switching the phase, i.e. the navigation mode, in response to the type and the duration of the current phase. Our findings reveal that the target-search efficiency increases with the particle's self-propulsion during the active phase and that, while the optimal duration of the passive case decreases monotonically with the activity, the optimal duration of the active phase displays a non-monotonic behavior.

Links between the three-dimensional movements of whale sharks (Rhincodon typus) and the bio-physical environment off a coral reef

BACKGROUND

Measuring coastal-pelagic prey fields at scales relevant to the movements of marine predators is challenging due to the dynamic and ephemeral nature of these environments. Whale sharks (Rhincodon typus) are thought to aggregate in nearshore tropical waters due to seasonally enhanced foraging opportunities. This implies that the three-dimensional movements of these animals may be associated with bio-physical properties that enhance prey availability. To date, few studies have tested this hypothesis.

METHODS

Here, we conducted ship-based acoustic surveys, net tows and water column profiling (salinity, temperature, chlorophyll fluorescence) to determine the volumetric density, distribution and community composition of mesozooplankton (predominantly euphausiids and copepods) and oceanographic properties of the water column in the vicinity of whale sharks that were tracked simultaneously using satellite-linked tags at Ningaloo Reef, Western Australia. Generalised linear mixed effect models were used to explore relationships between the 3-dimensional movement behaviours of tracked sharks and surrounding prey fields at a spatial scale of ~ 1 km.

RESULTS

We identified prey density as a significant driver of horizontal space use, with sharks occupying areas along the reef edge where densities were highest. These areas were characterised by complex bathymetry such as reef gutters and pinnacles. Temperature and salinity profiles revealed a well-mixed water column above the height of the bathymetry (top 40 m of the water column). Regions of stronger stratification were associated with reef gutters and pinnacles that concentrated prey near the seabed, and entrained productivity at local scales (~ 1 km). We found no quantitative relationship between the depth use of sharks and vertical distributions of horizontally averaged prey density. Whale sharks repeatedly dove to depths where spatially averaged prey concentration was highest but did not extend the time spent at these depth layers.

CONCLUSIONS

Our work reveals previously unrecognized complexity in interactions between whale sharks and their zooplankton prey.

Optimizing search processes with stochastic resetting on the pseudofractal scale-free web

The pseudofractal scale-free web (PSFW) is a well-known model for a scale-free network with small-world characteristics. Understanding the dynamic properties of this network can provide valuable insights into dynamic processes occurring in general scale-free and small-world networks. In this study we investigate search processes using discrete-time random walks on the PSFW to reveal the impact of the resetting position on optimizing search efficiency, as measured by the mean first-passage time (MFPT). At each step the walker has two options: with a probability of 1-γ, it moves to one of the neighboring sites, and with a probability of γ, it resets to the predefined resetting position. We explore various choices for the resetting position, present rigorous results for the MFPT to a given node of the network, determine the optimal resetting probability γ^{*} where the MFPT reaches its minimum, and evaluate the ratio of the minimum for MFPT to the MFPT without resetting for each case. Results show that, in large PSFWs, both the degree of the resetting position and the distance between the target and the resetting position significantly affect the search efficiency. A higher degree of the resetting position leads to a slower convergence of the walker to the target, while a greater distance between the target and the resetting position also results in a slower convergence. Additionally, we observe that resetting to a vertex randomly selected from the stationary distribution can significantly expedite the process of the walker reaching the target. The findings presented in this study shed light on optimizing stochastic search processes on large networks, offering valuable insights into improving search efficiency in real-world applications, where the target node's location is unknown.

Characteristics of daily foraging activity of Camponotus japonicus via time series analysis

Social insects often share tasks among individuals. In this study, we analyzed the foraging activity of ants (Camponotus japonicus) and recorded the daily passage event counts of individual workers between a nest chamber and a foraging arena in five monodomous colonies. We proposed two hypotheses on the time series of foraging frequency by individual worker ants as follows: (i) for the time series of foraging frequency by individual worker ants, the foraging frequency on a certain day could be expressed by the product of the foraging frequency on the previous day and the exponential of a random number. (ii) The random numbers are correlated between some pairs of worker ants. The results for the five tested ant colonies showed that the probability of total daily passage counts (the sum of an individual's passage count) followed a log-normal distribution. The worker ants behaved differently in terms of active days and foraging frequency. However, for > 54% of the worker ants, the probability of the daily passage count was characterized by a log-normal distribution, and these worker ants performed > 72% of the tasks in each colony. Furthermore, for > 73% of the worker ants, the time development of the passage count was mathematically modeled; the logarithmic first difference between the passage counts on a certain day and those on the previous day was a random normal variable. These results support hypothesis (i). Additionally, the random numbers that were equivalent to the logarithmic first difference were correlated for some pairs of worker ants. These results support hypothesis (ii).

The biology and ecology of the basking shark: A review

Here we review the literature on the basking shark (Cetorhinus maximus, Gunnerus, 1765), well known as the second largest extant shark (and fish) species globally. Previous reviews were published by Kunzlik in 1988 and Sims in 2008, but in the last 15 years modern electronic and DNA sequencing technologies have resulted in considerable advances in our knowledge of the species' behaviour and ecology. Basking sharks are planktivores and under appropriate conditions spend prolonged periods at the ocean surface feeding on copepod prey that primarily make up their diet, the behaviour that gave rise to their common name. In general, they are migratory and move into higher latitude waters during the summer months, when loose surface-feeding aggregations may form at favoured sites, the best known of which at present occur at hotspots on the west coasts of Britain and Ireland. The species is found circumglobally in temperate waters, but they are also now known on occasion to migrate at depth between northern and southern hemispheres, as well as across oceans within the northern hemisphere. In the past basking shark were more abundant across much of their range, but, consequent on targeted fisheries and in some places intentional eradication, became everywhere scarce, with recent population recovery in the north-east Atlantic being the result of protective measures initiated in the 1990s. Despite their charismatic nature, some of their most fundamental biological processes including copulation, gestation and birth remain largely unknown, due to their migratory and often deep-water lifestyle. In contrast, the deployment of small-scale archival and satellite tags has revealed the details of both broadscale migratory movements and horizontal and vertical foraging behaviours. Recent genetic studies support evidence suggesting a degree of site fidelity in relation to seasonal feeding grounds, which likely explains why in the past local populations have collapsed following periods of intensive fishing. Other recent research using aerial drones and towed cameras has revealed within loose feeding aggregations elements of social behaviour that may have a courtship function as well as enhance feeding efficiency.

Fluctuating landscapes and heavy tails in animal behavior

Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales. This immense variability hampers quantitative reasoning and renders the identification of universal principles elusive. Through data analysis and theory, we here show that slow non-ergodic drives generally give rise to heavy-tailed statistics in behaving animals. We leverage high-resolution recordings of C. elegans locomotion to extract a self-consistent reduced order model for an inferred reaction coordinate, bridging from sub-second chaotic dynamics to long-lived stochastic transitions among metastable states. The slow mode dynamics exhibits heavy-tailed first passage time distributions and correlation functions, and we show that such heavy tails can be explained by dynamics on a time-dependent potential landscape. Inspired by these results, we introduce a generic model in which we separate faster mixing modes that evolve on a quasi-stationary potential, from slower non-ergodic modes that drive the potential landscape, and reflect slowly varying internal states. We show that, even for simple potential landscapes, heavy tails emerge when barrier heights fluctuate slowly and strongly enough. In particular, the distribution of first passage times and the correlation function can asymptote to a power law, with related exponents that depend on the strength and nature of the fluctuations. We support our theoretical findings through direct numerical simulations.

Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks

Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues. Whether or not such control is achieved by utilizing different movement strategies in different tissues remains poorly understood. Liver-localized CD8 T cells perform correlated random walks  --- a type of a Brownian walk -- in liver sinusoids but in some condition these T cells may also perform Levy flights -- rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-localized CD8 T cells, specific to Toxoplasma gondii, perform generalized Levy walks -- a walk type in which T cells alternate pausing and displacing long distances --- which may indicate that brain is a unique organ where T cells exhibit movement strategies different from other tissues. Methods.  We quantified movement patterns of brain-localized Plasmodium berghei-specific CD4 and CD8 T cells by using well-established statistical and computational methods. Results.  We found that T cells change their movement pattern with time since infection and that CD4 T cells move faster and turn less than CD8 T cells. Importantly, both CD4 and CD8 T cells move in the brain by correlated random walks without long displacements challenging previous observations. We have also re-analyzed the movement data of brain-localized CD8 T cells in T. gondii-infected mice and found no evidence of Levy walks. We hypothesize that the previous conclusion of Levy walks of T. gondii-specific CD8 T cells in the brain was reached due to missing time-frames in the data that create an impression of large movement lengths between assumed-to-be-sequential movements.  Conclusion. Our results suggests that movement strategies of CD8 T cells are largely similar between LNs, liver, and the brain and consistent with correlated random walks and not Levy walks.

Lévy movements and a slowly decaying memory allow efficient collective learning in groups of interacting foragers

Many animal species benefit from spatial learning to adapt their foraging movements to the distribution of resources. Learning involves the collection, storage and retrieval of information, and depends on both the random search strategies employed and the memory capacities of the individual. For animals living in social groups, spatial learning can be further enhanced by information transfer among group members. However, how individual behavior affects the emergence of collective states of learning is still poorly understood. Here, with the help of a spatially explicit agent-based model where individuals transfer information to their peers, we analyze the effects on the use of resources of varying memory capacities in combination with different exploration strategies, such as ordinary random walks and Lévy flights. We find that individual Lévy displacements associated with a slow memory decay lead to a very rapid collective response, a high group cohesion and to an optimal exploitation of the best resource patches in static but complex environments, even when the interaction rate among individuals is low.

Artificial fish nurseries can restore certain nursery characteristics in marine urban habitats

Port areas are subjected to multiple anthropic pressures that directly impact residing marine communities and deprive them of most of their essential ecological functions. Several global projects aim to rehabilitate certain ecosystem functions in port areas, such as a fish nursery function, by installing artificial fish nurseries (AFN). In theory, AFNs increase fish biodiversity and juvenile fish abundance in port areas, but studies on this subject remain scarce. Thus, the present study aimed to examine whether the use of such AFNs could restore part of the nursery function of natural habitats by increasing fish and juvenile abundance, and by decreasing predation intensity compared to bare docks. Two years of monitoring on AFNs showed they hosted 2.1 times more fish than on control docks and up to 2.4 more fish juveniles. Fish community structures were influenced by both treatment (AFN and Control) and year of monitoring. In general, AFNs hosted a greater taxonomic diversity of fish than controls. The predation intensity around these structures was significantly lower in the AFNs than in controls. Part of the definition of a fish nursery was thus verified, indicating that AFNs might be an effective restoration tool. However, we also noted that total fish abundance and Young of the Year (YOY) abundance decreased in controls, possibly due to a concentration effect. Further detailed monitoring is necessary to distinguish between these effects.

Linking neural circuits to the mechanics of animal behavior in Drosophila larval locomotion

The motions that make up animal behavior arise from the interplay between neural circuits and the mechanical parts of the body. Therefore, in order to comprehend the operational mechanisms governing behavior, it is essential to examine not only the underlying neural network but also the mechanical characteristics of the animal's body. The locomotor system of fly larvae serves as an ideal model for pursuing this integrative approach. By virtue of diverse investigation methods encompassing connectomics analysis and quantification of locomotion kinematics, research on larval locomotion has shed light on the underlying mechanisms of animal behavior. These studies have elucidated the roles of interneurons in coordinating muscle activities within and between segments, as well as the neural circuits responsible for exploration. This review aims to provide an overview of recent research on the neuromechanics of animal locomotion in fly larvae. We also briefly review interspecific diversity in fly larval locomotion and explore the latest advancements in soft robots inspired by larval locomotion. The integrative analysis of animal behavior using fly larvae could establish a practical framework for scrutinizing the behavior of other animal species.

Modeling three-dimensional T-cell motility using clustering and hidden Markov models

Recent advances in imaging technologies now allow for real-time tracking of fast-moving immune cells as they search for targets such as pathogens and tumor cells through complex three-dimensional tissues. Cytotoxic T cells are specialized immune cells that continually scan tissues for such targets to engage and kill, and have emerged as the principle mediators of breakthrough immunotherapies against cancers. Modeling the way these T cells move is of great value in furthering our understanding of their collective search efficiency. T-cell motility is characterized by heterogeneity at two levels: (a) Individual cells display different distributions of translational speeds and turning angles, and (b) each cell can during a given track, its motility, switch between local search and directional motion. Despite a likely considerable influence on a motile population's search performance, statistical models that accurately capture both such heterogeneities in a distinguishing manner are lacking. Here, we model three-dimensional T-cell trajectories through a spherical representation of their incremental steps and compare model outputs to real-world motility data from primary T cells navigating physiological environments. T cells in a population are clustered based on their directional persistence and characteristic "step lengths" therein capturing between-cell heterogeneity. The motility dynamics of cells within each cluster are individually modeled through hidden Markov model to capture within-cell transitions between local and more extensive search patterns. We explore the importance of explicitly capturing altered motility patterns when cells lie in close proximity to one another, through a non-homogenous hidden Markov model.

Virtual prey with Lévy motion are preferentially attacked by predatory fish

Of widespread interest in animal behavior and ecology is how animals search their environment for resources, and whether these search strategies are optimal. However, movement also affects predation risk through effects on encounter rates, the conspicuousness of prey, and the success of attacks. Here, we use predatory fish attacking a simulation of virtual prey to test whether predation risk is associated with movement behavior. Despite often being demonstrated to be a more efficient strategy for finding resources such as food, we find that prey displaying Lévy motion are twice as likely to be targeted by predators than prey utilizing Brownian motion. This can be explained by the predators, at the moment of the attack, preferentially targeting prey that were moving with straighter trajectories rather than prey that were turning more. Our results emphasize that costs of predation risk need to be considered alongside the foraging benefits when comparing different movement strategies.

Plasmodium sporozoite search strategy to locate hotspots of blood vessel invasion

Plasmodium sporozoites actively migrate in the dermis and enter blood vessels to infect the liver. Despite their importance for malaria infection, little is known about these cutaneous processes. We combine intravital imaging in a rodent malaria model and statistical methods to unveil the parasite strategy to reach the bloodstream. We determine that sporozoites display a high-motility mode with a superdiffusive Lévy-like pattern known to optimize the location of scarce targets. When encountering blood vessels, sporozoites frequently switch to a subdiffusive low-motility behavior associated with probing for intravasation hotspots, marked by the presence of pericytes. Hence, sporozoites present anomalous diffusive motility, alternating between superdiffusive tissue exploration and subdiffusive local vessel exploitation, thus optimizing the sequential tasks of seeking blood vessels and pericyte-associated sites of privileged intravasation.

Optimal foraging strategies for mutually avoiding competitors

Many animals are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Lévy distribution. Previous studies have shown that, under sparse and random resource conditions, solitary non-destructive (with regenerating resources) foragers perform a maximally efficient search with Lévy exponent μ equal to 2, while for destructive foragers, efficiency decreases with μ monotonically and there is no optimal μ. However, in nature, there also exist situations where multiple foragers, displaying avoidance behavior, interact with each other competitively. To understand the effects of such competition, we develop a stochastic agent-based simulation that models competitive foraging among mutually avoiding individuals by incorporating an avoidance zone, or territory, of a certain size around each forager which is not accessible for foraging by other competitors. For non-destructive foraging, our results show that with increasing size of the territory and number of agents the optimal Lévy exponent is still approximately 2 while the overall efficiency of the search decreases. At low values of the Lévy exponent, however, increasing territory size actually increases efficiency. For destructive foraging, we show that certain kinds of avoidance can lead to qualitatively different behavior from solitary foraging, such as the existence of an optimal search with 1<μ<2. Finally, we show that the variance among the efficiencies of the agents increases with increasing Lévy exponent for both solitary and competing foragers, suggesting that reducing variance might be a selective pressure for foragers adopting lower values of μ. Taken together, our results suggest that, for multiple foragers, mutual avoidance and efficiency variance among individuals can lead to optimal Lévy searches with exponents different from those for solitary foragers.

Universal singularities of anomalous diffusion in the Richardson class

Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to contrasting environmental features (hindering or favoring the motion, respectively), they are both observed in systems ranging from the micro- to the cosmological scale. Here we show how a model encompassing sub- and superdiffusion in an inhomogeneous environment exhibits a critical singularity in the normalized generator of the cumulants. The singularity originates directly and exclusively from the asymptotics of the non-Gaussian scaling function of displacement, and the independence from other details confers it a universal character. Our analysis, based on the method first applied by Stella et al. [Phys. Rev. Lett. 130, 207104 (2023)10.1103/PhysRevLett.130.207104], shows that the relation connecting the scaling function asymptotics to the diffusion exponent characteristic of processes in the Richardson class implies a nonstandard extensivity in time of the cumulant generator. Numerical tests fully confirm the results.

Entropy and Fractal Techniques for Monitoring Fish Behaviour and Welfare in Aquacultural Precision Fish Farming-A Review

In a non-linear system, such as a biological system, the change of the output (e.g., behaviour) is not proportional to the change of the input (e.g., exposure to stressors). In addition, biological systems also change over time, i.e., they are dynamic. Non-linear dynamical analyses of biological systems have revealed hidden structures and patterns of behaviour that are not discernible by classical methods. Entropy analyses can quantify their degree of predictability and the directionality of individual interactions, while fractal dimension (FD) analyses can expose patterns of behaviour within apparently random ones. The incorporation of these techniques into the architecture of precision fish farming (PFF) and intelligent aquaculture (IA) is becoming increasingly necessary to understand and predict the evolution of the status of farmed fish. This review summarizes recent works on the application of entropy and FD techniques to selected individual and collective fish behaviours influenced by the number of fish, tagging, pain, preying/feed search, fear/anxiety (and its modulation) and positive emotional contagion (the social contagion of positive emotions). Furthermore, it presents an investigation of collective and individual interactions in shoals, an exposure of the dynamics of inter-individual relationships and hierarchies, and the identification of individuals in groups. While most of the works have been carried out using model species, we believe that they have clear applications in PFF. The review ends by describing some of the major challenges in the field, two of which are, unsurprisingly, the acquisition of high-quality, reliable raw data and the construction of large, reliable databases of non-linear behavioural data for different species and farming conditions.

A Sublethal Concentration of Sulfoxaflor Has Minimal Impact on Buff-Tailed Bumblebee (Bombus terrestris) Locomotor Behaviour under Aversive Conditioning

Pesticide exposure has been cited as a key threat to insect pollinators. Notably, a diverse range of potential sublethal effects have been reported in bee species, with a particular focus on effects due to exposure to neonicotinoid insecticides. Here, a purpose-built thermal-visual arena was used in a series of pilot experiments to assess the potential impact of approximate sublethal concentrations of the next generation sulfoximine insecticide sulfoxaflor (5 and 50 ppb) and the neonicotinoid insecticides thiacloprid (500 ppb) and thiamethoxam (10 ppb), on the walking trajectory, navigation and learning abilities of the buff-tailed bumblebee (Bombus terrestris audax) when subjected to an aversive conditioning task. The results suggest that only thiamethoxam prevents forager bees from improving in key training parameters (speed and distanced travelled) within the thermal visual arena. Power law analyses further revealed that a speed-curvature power law, previously reported as being present in the walking trajectories of bumblebees, is potentially disrupted under thiamethoxam (10 ppb) exposure, but not under sulfoxaflor or thiacloprid exposure. The pilot assay described provides a novel tool with which to identify subtle sublethal pesticide impacts, and their potential causes, on forager bees, that current ecotoxicological tests are not designed to assess.

Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Noise-induced escape from metastable states governs a plethora of transition phenomena in physics, chemistry, and biology. While the escape problem in the presence of thermal Gaussian noise has been well understood since the seminal works of Arrhenius and Kramers, many systems, in particular living ones, are effectively driven by non-Gaussian noise for which the conventional theory does not apply. Here we present a theoretical framework based on path integrals that allows the calculation of both escape rates and optimal escape paths for a generic class of non-Gaussian noises. We find that non-Gaussian noise always leads to more efficient escape and can enhance escape rates by many orders of magnitude compared with thermal noise, highlighting that away from equilibrium escape rates cannot be reliably modelled based on the traditional Arrhenius-Kramers result. Our analysis also identifies a new universality class of non-Gaussian noises, for which escape paths are dominated by large jumps.

Common features in spatial livestock disease transmission parameters

The risk of epidemic spread of diseases in livestock poses a threat to animal and often also human health. Important for the assessment of the effect of control measures is a statistical model quantification of between-farm transmission during epidemics. In particular, quantification of the between-farm transmission kernel has proven its importance for a range of different diseases in livestock. In this paper we explore if a comparison of the different transmission kernels yields further insight. Our comparison identifies common features that connect across the different pathogen-host combinations analyzed. We conjecture that these features are universal and thereby provide generic insights. Comparison of the shape of the spatial transmission kernel suggests that, in absence of animal movement bans, the distance dependence of transmission has a universal shape analogous to Lévy-walk model descriptions of human movement patterns. Also, our analysis suggests that interventions such as movement bans and zoning, through their impact on these movement patterns, change the shape of the kernel in a universal fashion. We discuss how the generic insights suggested can be of practical use for assessing risks of spread and optimizing control measures, in particular when outbreak data is scarce.

Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations

Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters' contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude.

Ants combine systematic meandering and correlated random walks when searching for unknown resources

Animal search movements are typically assumed to be mostly random walks, although non-random elements may be widespread. We tracked ants (Temnothorax rugatulus) in a large empty arena, resulting in almost 5 km of trajectories. We tested for meandering by comparing the turn autocorrelations for empirical ant tracks and simulated, realistic Correlated Random Walks. We found that 78% of ants show significant negative autocorrelation around 10 mm (3 body lengths). This means that turns in one direction are likely followed by turns in the opposite direction after this distance. This meandering likely makes the search more efficient, as it allows ants to avoid crossing their own paths while staying close to the nest, avoiding return-travel time. Combining systematic search with stochastic elements may make the strategy less vulnerable to directional inaccuracies. This study is the first to find evidence for efficient search by regular meandering in a freely searching animal.

Scale-free behavioral dynamics directly linked with scale-free cortical dynamics

Naturally occurring body movements and collective neural activity both exhibit complex dynamics, often with scale-free, fractal spatiotemporal structure. Scale-free dynamics of both brain and behavior are important because each is associated with functional benefits to the organism. Despite their similarities, scale-free brain activity and scale-free behavior have been studied separately, without a unified explanation. Here, we show that scale-free dynamics of mouse behavior and neurons in the visual cortex are strongly related. Surprisingly, the scale-free neural activity is limited to specific subsets of neurons, and these scale-free subsets exhibit stochastic winner-take-all competition with other neural subsets. This observation is inconsistent with prevailing theories of scale-free dynamics in neural systems, which stem from the criticality hypothesis. We develop a computational model which incorporates known cell-type-specific circuit structure, explaining our findings with a new type of critical dynamics. Our results establish neural underpinnings of scale-free behavior and clear behavioral relevance of scale-free neural activity.

Modified Marine Predators Algorithm hybridized with teaching-learning mechanism for solving optimization problems

Marine Predators Algorithm (MPA) is a newly nature-inspired meta-heuristic algorithm, which is proposed based on the Lévy flight and Brownian motion of ocean predators. Since the MPA was proposed, it has been successfully applied in many fields. However, it includes several shortcomings, such as falling into local optimum easily and precocious convergence. To balance the exploitation and exploration ability of MPA, a modified marine predators algorithm hybridized with teaching-learning mechanism is proposed in this paper, namely MTLMPA. Compared with MPA, the proposed MTLMPA has two highlights. Firstly, a kind of teaching mechanism is introduced in the first phase of MPA to improve the global searching ability. Secondly, a novel learning mechanism is introduced in the third phase of MPA to enhance the chance encounter rate between predator and prey and to avoid premature convergence. MTLMPA is verified by 23 benchmark numerical testing functions and 29 CEC-2017 testing functions. Experimental results reveal that the MTLMPA is more competitive compared with several state-of-the-art heuristic optimization algorithms.

First encounters on Watts-Strogatz networks and Barabási-Albert networks

The Watts-Strogatz networks are important models that interpolate between regular lattices and random graphs, and Barabási-Albert networks are famous models that explain the origin of the scale-free networks. Here, we consider the first encounters between two particles (e.g., prey A and predator B) embedded in the Watts-Strogatz networks and the Barabási-Albert networks. We address numerically the mean first-encounter time (MFET) while the two particles are moving and the mean first-passage time (MFPT) while the prey is fixed, aiming at uncovering the impact of the prey's motion on the encounter time, and the conditions where the motion of the prey would accelerate (or slow) the encounter between the two particles. Different initial conditions are considered. In the case where the two particles start independently from sites that are selected randomly from the stationary distribution, on the Barabási-Albert networks, the MFET is far less than the MFPT, and the impact of prey's motion on the encounter time is enormous, whereas, on the Watts-Strogatz networks (including Erdős-Rényi random networks), the MFET is about 0.5-1 times the MFPT, and the impact of prey's motion on the encounter time is relatively small. We also consider the case where prey A starts from a fixed site and the predator starts from a randomly drawn site and present the conditions where the motion of the prey would accelerate (or slow) the encounter between the two particles. The relation between the MFET (or MFPT) and the average path length is also discussed.

A guide to area-restricted search: a foundational foraging behaviour

Area-restricted search is the capacity to change search effort adaptively in response to resource encounters or expectations, from directional exploration (global, extensive search) to focused exploitation (local, intensive search). This search pattern is used by numerous organisms, from worms and insects to humans, to find various targets, such as food, mates, nests, and other resources. Area-restricted search has been studied for at least 80 years by ecologists, and more recently in the neurological and psychological literature. In general, the conditions promoting this search pattern are: (1) clustered resources; (2) active search (e.g. not a sit-and-wait predator); (3) searcher memory for recent target encounters or expectations; and (4) searcher ignorance about the exact location of targets. Because area-restricted search adapts to resource encounters, the search can be performed at multiple spatial scales. Models and experiments have demonstrated that area-restricted search is superior to alternative search patterns that do not involve a memory of the exact location of the target, such as correlated random walks or Lévy walks/flights. Area-restricted search is triggered by sensory cues whereas concentrated search in the absence of sensory cues is associated with other forms of foraging. Some neural underpinnings of area-restricted search are probably shared across metazoans, suggesting a shared ancestry and a shared solution to a common ecological problem of finding clustered resources. Area-restricted search is also apparent in other domains, such as memory and visual search in humans, which may indicate an exaptation from spatial search to other forms of search. Here, we review these various aspects of area-restricted search, as well as how to identify it, and point to open questions.

Foraging in heterogeneous landscapes: variation in movement patterns of a tropical sand-bubbler crab

Acquiring food in heterogeneous landscapes presents a challenge to many foragers, as searching for food in an optimal manner is difficult in spatially and temporally variable environments. Investigating individual foraging patterns can elucidate how environmental variations at different scales constrain or select for energy-optimizing movements, which can inform conservation and management strategies by identifying spatio-temporal variations in species’ habitat use. To test how such movements vary with environmental conditions, we investigated foraging patterns of the deposit-feeding sand-bubbler crab, Scopimera intermedia Balss, 1934 at multiple spatial and temporal scales on soft sediment shores in Hong Kong. On a broad, annual, scale the crabs produced foraging tracks of different length and foraged over different areas around their burrows between hot and cool seasons. Although foraging movements of the crabs were slower and more restricted during the cool season, probably due to low environmental temperatures, foraging areas during the hot season were larger but limited by increasing conspecific interactions. Over a smaller scale at which the crabs make movement decisions, parameters such as turning angle and speed were variable, even within individual foraging excursions. Such variations appeared to be responses to small-scale variations in sediment food patches, which resulted in the crabs employing multiple movement modes. This context-dependent foraging strategy enables the crabs to feed for a longer time in food-rich patches compared with a fixed strategy and is, therefore, critical for species living in environments such as intertidal sediments, where food distribution is heterogeneous and foraging time is constrained by the tide.

Effect of the search space dimensionality for finding close and faraway targets in random searches

We investigate the dependence on the search space dimension of statistical properties of random searches with Lévy α-stable and power-law distributions of step lengths. We find that the probabilities to return to the last target found (P_{0}) and to encounter faraway targets (P_{L}), as well as the associated Shannon entropy S, behave as a function of α quite differently in one (1D) and two (2D) dimensions, a somewhat surprising result not reported until now. While in 1D one always has P_{0}≥P_{L}, an interesting crossover takes place in 2D that separates the search regimes with P_{0}>P_{L} for higher α and P_{0}<P_{L} for lower α, depending on the initial distance to the last target found. We also obtain in 2D a maximum in the entropy S for α∈(0,2], not observed in 1D apart from the trivial α→0 ballistic limit. Improving the understanding of the role of dimensionality in random searches is relevant in diverse contexts, as in the problem of encounter rates in biology and ecology.

Glioblastoma hijacks neuronal mechanisms for brain invasion

Glioblastomas are incurable tumors infiltrating the brain. A subpopulation of glioblastoma cells forms a functional and therapy-resistant tumor cell network interconnected by tumor microtubes (TMs). Other subpopulations appear unconnected, and their biological role remains unclear. Here, we demonstrate that whole-brain colonization is fueled by glioblastoma cells that lack connections with other tumor cells and astrocytes yet receive synaptic input from neurons. This subpopulation corresponds to neuronal and neural-progenitor-like tumor cell states, as defined by single-cell transcriptomics, both in mouse models and in the human disease. Tumor cell invasion resembled neuronal migration mechanisms and adopted a Lévy-like movement pattern of probing the environment. Neuronal activity induced complex calcium signals in glioblastoma cells followed by the de novo formation of TMs and increased invasion speed. Collectively, superimposing molecular and functional single-cell data revealed that neuronal mechanisms govern glioblastoma cell invasion on multiple levels. This explains how glioblastoma's dissemination and cellular heterogeneity are closely interlinked.

Living on fire: Deactivating fire coral polyps for larval settlement and symbiosis in the fire coral-associated barnacle Wanella milleporae (Thoracicalcarea: Wanellinae)

Symbiosis is increasingly recognized as being an important component in marine systems, and many such relationships are initiated when free-swimming larvae of one partner settle and become sedentary on a host partner. Therefore, several crucial questions emerge such as the larva's mechanism of locating a host, selection of substratum and finally settlement on the surface of its future partner. Here, we investigated these mechanisms by studying how larvae of the fire coral-associated barnacle Wanella milleporae move, settle and establish symbiosis with their host, Millepora tenera. Cyprids of W. milleporae possess a pair of specialized antennules with bell-shaped attachment discs that enable them to explore and settle superficially on the hostile surface of the fire coral. Intriguingly, the stinging polyps of the fire coral remain in their respective pores when the cyprids explore the fire coral surface. Even when cyprids come into contact with the nematocysts on the extended stinging polyps during the exploratory phase, no immobilization effects against the cyprids were observed. The exploratory phase of Wanella cyprids can be divided into a sequence of wide searching (large step length and high walking speed), close searching (small step length and low speed) and inspection behavior, eventually resulting in permanent settlement and metamorphosis. After settlement, xenogeneic interactions occur between the fire coral and the newly metamorphosed juvenile barnacle. This involved tissue necrosis and regeneration in the fire coral host, leading to a callus ring structure around the juvenile barnacle, enhancing survival rate after settlement. The complex exploratory and settlement patterns and interactions documented here represent a breakthrough in coral reef symbiosis studies to show how invertebrates start symbiosis with fire corals.

Bioinspired Environment Exploration Algorithm in Swarm Based on Lévy Flight and Improved Artificial Potential Field

Inspired by the behaviour of animal populations in nature, we propose a novel exploration algorithm based on Lévy flight (LF) and artificial potential field (APF). The agent is extended to the swarm level using the APF method through the LF search environment. Virtual leaders generate moving steps to explore the environment through the LF mechanism. To achieve collision-free movement in an unknown constrained environment, a swarm-following mechanism is established, which requires the agents to follow the virtual leader to carry out the LF. The proposed method, combining the advantages of LF and APF which achieve the effect of flocking in an exploration environment, does not rely on complex sensors for environment labelling, memorising, or huge computing power. Agents simply perform elegant and efficient search behaviours as natural creatures adapt to the environment and change formations. The method is especially suitable for the camouflaged flocking exploration environment of bionic robots such as flapping drones. Simulation experiments and real-world experiments on E-puck2 robots were conducted to evaluate the effectiveness of the proposed LF-APF algorithm.

Activity-Induced Enhancement of Superdiffusive Transport in Bacterial Turbulence

Superdiffusion processes significantly promote the transport of tiny passive particles within biological fluids. Activity, one of the essential measures for living matter, however, is less examined in terms of how and to what extent it can improve the diffusivity of the moving particles. Here, bacterial suspensions are confined within the microfluidic channel at the state of bacterial turbulence, and are tuned to different activity levels by oxygen consumption in control. Systematic measurements are conducted to determine the superdiffusion exponent, which characterizes the diffusivity strength of tracer particles, depending on the continuously injecting energy converted to motile activity from swimming individuals. Higher activity is quantified to drastically enhance the superdiffusion process of passive tracers in the short-time regime. Moreover, the number density of the swimming bacteria is controlled to contribute to the field activity, and then to strengthen the super-diffusivity of tracers, distinguished by regimes with and without collective motion of interacting bacteria. Finally, the non-slip surfaces of the microfluidic channel lower the superdiffusion of immersed tracers due to the resistance, with the small diffusivity differing from the counterpart in the bulk. The findings here suggest ways of controlled diffusion and transport of substances within the living system with different levels of nutrition and resources and boundary walls, leading to efficient mixing, drug delivery and intracellular communications.

Drivers of fine-scale diurnal space use by a coral-reef mesopredatory fish

The habitat preferences of many reef fishes are well established, but the use of space within these habitats by non-site-attached species is poorly studied. The authors examined the space use of a functionally important mesopredator, graysby (Cephalopholis cruentata), on six patch reefs in the Florida Keys. A 1 m² -scale grid was constructed on each reef and 16 individual C. cruentata were tracked diurnally in situ to identify space use. At the patch reef scale, larger C. cruentata were more active and had larger observed home ranges, although home ranges were also affected by fish density and the abundances of prey and predators. The total time in each 1 m² grid cell was regressed against a range of fine-scale biotic variables, including multiple variables derived from structure-from-motion three-dimensional digital reconstructions of each reef. Nonetheless, time in grid cells (preferred microhabitats) was only significantly positively correlated with the height of carbonate structures, likely because the cavities they enclose are particularly suitable for predator avoidance, resting and ambushing prey. The ongoing flattening of reefs in the region caused by negative carbonate budgets is thus likely to have significant effects on the abundance and space use of C. cruentata. In addition to examining spatial patterns, we analysed C. cruentata waiting times in each grid cell before moving. These times were best approximated by a truncated power-law (heavy-tailed) distribution, indicating a "bursty" pattern of relatively long periods of inactivity interspersed with multiple periods of activity. Such a pattern has previously been identified in a range of temperate ambush predators, and the authors extend this move-wait behaviour, which may optimize foraging success, to a reef fish for the first time. Understanding how C. cruentata uses space and time is critical to fully identify their functional role and better predict the implications of fishing and loss of reef structure.

Search Foraging Strategies of Migratory Raptors Under Different Environmental Conditions

Several studies have shown in different organisms how their movements can be fitted to different patterns to optimize search of food resources. According to abundance and availability of resources, different strategies will be optimal, such as Lévy and Brownian random search. We analyze the movement patterns of four species of migratory raptors with different degrees of ecological specialization in diet during the breeding and wintering periods to evaluate the differences according to species and season: the Egyptian Vulture, the Short-toed Snake Eagle, the Booted Eagle, and the Red Kite. From GPS locations, we obtained a set of segments and lengths that were analyzed to verify their fitting to the functions of Lévy and Brownian strategies. Egyptian Vulture’s trajectories fitted to both patterns during the breeding period, whereas during the wintering period most trajectories fitted a Brownian pattern. In the case of the Short-toed Eagle, fit was greater to a Lévy strategy throughout the year, while Booted Eagles and Red Kites exhibited a combination of search patterns. These differences could be accounted for different feeding strategies and environmental context over the annual cycle. In species with a specialized diet (i.e., Short-toed Eagle) the Lévy pattern would maximize the encounters with scarce and unpredictable resources, whereas for species with a broad trophic niche (i.e., Booted Eagle and Red Kite), movements could be adapted to exploit different resources according to their abundance. Scavengers like the Egyptian Vulture shift also between search strategies according to the distribution of carrion. Therefore, the analysis of food search patterns can be used as an indirect indicator to track changes in food availability across a broad range of environmental conditions. This is particularly important under the current context of global change which is largely expected to affect migratory species that spend their vital cycle in distant areas.

Anomalous band center localization in the one-dimensional Anderson model with a disordered distribution of infinite variance

We perform a detailed numerical study of the influence of distributions without a finite second moment on the Lyapunov exponent through the one-dimensional tight-binding Anderson model with diagonal disorder. Using the transfer matrix parametrization method and considering a specific distribution function, we calculate the Lyapunov exponent numerically and demonstrate its relation with the fractional lower order moments of the disorder probability density function. For the lower order of moments of disorder distribution with an infinite variance, we obtain the anomalous behavior near the band center.

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

The existence of landscape constraints in the home range of living organisms that adopt Lévy-flight movement patterns, prevents them from making arbitrarily large displacements. Their random movements indeed occur in a finite space with an upper bound. In order to make realistic models, by introducing exponentially truncated Lévy flights, such an upper bound can thus be taken into account in the reaction-diffusion models. In this work, we have investigated the influence of the λ-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where λ is the truncation parameter. Analytical and numerical simulations show that depending on the value of λ, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of λ (λ≳0), the tails of the infective waves can decay algebraically leading to an exponential growth of the epidemic speed. In that case, the truncation has no impact on the superdiffusive epidemics. By increasing the value of λ, the algebraic decaying tails can be tamed leading to either an upper bound on the epidemic speed representing the maximum speed value or the generation of the infective waves of a constant shape propagating at a minimum constant speed as observed in the classical models (second-order diffusion epidemic models). Our findings suggest that the truncated fractional-order diffusion equations have the potential to model the epidemics of animals performing Lévy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics.